Vol. 319, No. 1, 2022

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Dirac cohomology and orthogonality relations for weight modules

Jing-Song Huang and Wei Xiao

Vol. 319 (2022), No. 1, 129–152
Abstract

The Schur orthogonality relations for finite-dimensional representations are generalized to weight modules of complex reductive Lie algebras by establishing the equality of the Euler–Poincaré pairing and the spinor pairing. We also show how to calculate these pairings by using Dirac cohomology.

Keywords
Dirac cohomology, weight module, Euler–Poincaré pairing, spinor pairing
Mathematical Subject Classification
Primary: 17B10
Milestones
Received: 16 March 2022
Revised: 27 May 2022
Accepted: 4 June 2022
Published: 28 August 2022
Authors
Jing-Song Huang
School of Science and Engineering
Chinese University of Hong Kong
Shenzhen
China
Wei Xiao
College of Mathematics and Statistics
Shenzhen Key Laboratory of Advanced Machine Learning and Applications
Shenzhen University
Shenzhen
China